Alliance between ousted president and Houthi rebels appears to crumble as Saleh says he wants talks with Saudi Arabia.

Yemen's Ali Abdullah Saleh has said he is open to talks with a Saudi-led coalition fighting Houthi rebels, in what the fighters called "a coup" against their fragile alliance with the ousted president.

Saleh made the comments on Saturday, as deadly infighting between forces loyal to him and Houthi rebels continued for a fourth day.

The former allies have been fighting the Saudi-led coalition for control of the country since March 2015, when Riyadh and several other Arab Sunni states intervened to reinstate the government of President Abd-Rabbu Mansour Hadi.

In October, the Saudi-led coalition bombing Yemen imposed a total blockade on the impoverished country after a rebel missile was shot down near Riyadh.

Last week, amid international pressure over the suffering of millions of Yemenis, some humanitarian aid was allowed to enter Yemen.

"I call on our brothers in neighbouring countries ... to stop their aggression and lift the blockade ... and we will turn the page," Saleh said in a televised speech on Saturday.

"We vow to our brothers and neighbours that, after a ceasefire is in place and the blockade is lifted ... we will hold dialogue directly through the legitimate authority represented by our parliament," added Saleh.

A Houthi spokesman was quick to denounce Saleh's comments, accusing the former president of staging a "coup".

"Saleh's speech is a coup against our alliance and partnership ... and exposed the deception of those who claim to stand against aggression," the spokesman said in a statement, carried by the rebels' Al Masirah TV.

Also responding to Saleh's speech, Houthi leader Abdel-Malek al-Houthi stressed the need for dialogue and called on the former president to "be more mature".

However, in a statement, Saleh's General People's Congress (GPC) ordered their supporters to "defend their homeland, their revolution, and their unity".

Sanaa infighting

The Houthi rebels, who are believed to be backed by Iran, stormed Yemen's capital, Sanaa, in September 2014. They seized control of the city and eventually led Hadi to flee.

In May 2015, following Saudi-led coalition air raids on his home in Sanaa, Saleh officially announced for the first time the establishment of his alliance with the Houthis.

But the tactical alliance between Saleh, who was deposed five years ago, and the Houthis has often appeared fragile, with both groups suspicious of each other's ultimate motives and sharing little ideological ground.

In recent days, Sanaa has been shaken by escalating violence between Saleh's supporters and Houthi rebels.

At least 40 people have reportedly been killed since Wednesday, with residents now fearing a new front in an already devastating war.

On Saturday, Sanaa residents said that armed men from the GPC attacked Houthi-held government institutions, as clashes continued.

"What we are hearing is that Houthi gunmen have been pushed out of key positions in Sanaa," Peter Salisbury, a senior research fellow in the Middle East and North Africa Programme at Chatham House, said.

"They are now regrouping and massing forces on the outskirts of the capital. There are also the various tribal groups around Sanaa getting ready to fight with them, so it looks like things are going to get pretty serious in and around the capital in the coming days."

Salisbury also said that Saleh's comments were in effect an announcement of the end of his alliance with the Houthis.

"Both sides have been pretty harsh in their rhetoric over the last couple of days," said Salisbuty. "It seems there is no going back in terms of the splitting of that coalition."

Political analyst Ibrahim Qatabi agreed, saying that the Houthis and Saleh had only become allies "to overthrow" Hadi's government.

"We all knew all along that this day will have to come and that fighting between the Houthis and Saleh will have to break, so it is happening right now," he said.

"Saleh called on his supporters, loyalists and the professional army to declare war against the Houthis," he added.

Qatabi said it was very likely that Saleh's statement had the support of the Saudi-led coalition.

"I think it's very clear that maybe he wants to put one of his family members to share power with the current legitimate government," he said, referring to Hadi's administration.

"It seems to me there might be some collaboration between regional powers and Saleh, and maybe the legitimate government, to somehow overthrow the Houthis first and then have a serious political talk."

Saudi response

In a statement on Saturday, the Saudi-led coalition praised Saleh for "taking the lead" in the conflict.

"The decision by GPC to take the lead and their choice to side with their people will free Yemen of ... militias loyal to Iran," the statement carried by the official Saudi Press Agency said.

Salisbury said there are reports that Saleh's position "has been worked out through back channels" over the past few days, adding "that there is a deal in principle that people are willing to partake in".

"The question becomes how will the Saudi-led coalition respond, and how their allies on the ground will respond," he added.

"And for now, what seems to be happening is that they are not launching air strikes and they are not pushing on any of the front lines. It seems they are going to let this play out in Sanaa and see who comes out on top."

The war in Yemen is one of the worst humanitarian crises in the world, killing at least 10,000 people and leading to widespread hunger and disease.